TL;DR: In the work of the evolutionary cycle, man has to repeat what God has already done as discussed by the authors, he must himself create, in both the world of consciousness and of life, and thus bridges and makes contact with his environment, thereby gaining experience and sustenance.
Abstract: levels of the mental plane, and are beginning gradually to build the antahkarana, or the bridge between the Triad and the Personality . The power of the Ego can begin to make itself felt . Applicants for initiation and initiates up to the third initiation use both the sutratma and the antahkarana, employing them as a unit . The power of the Triad begins to pour through, thus energising all human activities upon the physical plane, and vitalising in ever increasing degree the man's thought forms . The key to the formation of the Mayavirupa is found in the right comprehension of the process . A Treatise on Cosmic Fire, pp. 959-960. It should be noted here that the bridging has to be done in the consciousness aspect, and concerns the continuity of man's awareness of life in all his various aspects . The energy which is used in connecting, in consciousness, the physical man and the astral body is focussed in the solar plexus . Speaking in symbolical terms, many today are carrying that bridge forward and linking the mind with the two aspects already linked . This thread of energy emanates from, or is anchored in, the head . A few people are steadily linking the soul and the mind, which in its turn is linked with the other two aspects . The soul energy, when linked with the other threads, has its anchor in the heart . A very few people (the initiates of the world) having effected all the lower syntheses, are now occupied with bringing about a still higher union with that triple Reality which uses the soul as its medium of expression, just as the soul in its turn is endeavouring to use its shadow, the threefold lower man. These distinctions and unifications are matters of form, 3 2 EDUCATION IN THE NEW AGE symbols in speech, and are used to express events and happenings in the world of energies and forces in connection with which man is definitely implicated . It is to these unifications that we refer when the subject of initiation is under consideration . The life thread, the silver cord or the sutratma, is, as far as man is concerned, dual in nature. The life thread proper, which is one of the two threads which constitute the antahkarana, is anchored in the heart, whilst the other thread which embodies the principle of consciousness, is anchored in the head . This you already know, but this I feel the need constantly to reiterate. In the work of the evolutionary cycle, however, man has to repeat what God has already done . He must himself create, in both the world of consciousness and of life . Like a spider, man spins connecting threads, and thus bridges and makes contact with his environment, thereby gaining experience and sustenance. The spider symbol is often used in the ancient occult books and the scriptures of India in connection with this activity of the human being . The threads which man creates are triple and with the two basic threads which have been created by the soul, constitute the five types of energy which make man a conscious human being . The triple threads created by man are anchored in the solar plexus, the head and the heart . When the astral body and the mind nature are beginning to function as a unit, and the soul also is consciously connected (do not forget that it is always unconsciously linked) , an extension of this fivefold thread -the basic two and the human three-is carried to the throat centre ; when that occurs man can become a conscious creator on the physical plane . From these major lines of energy lesser lines can radiate at will . It is upon this knowledge that all future intelligent psychic unfoldment must be based . In the above paragraph and its implications you have a brief and inadequate statement as to the Science of the THE OBJECTIVE OF THE NEW EDUCATION 3 3 Antahkarana . I have endeavoured to express this in terms, symbolic if you will, which will convey some general idea of the process to your minds . We can learn much through the use of the pictorial and visual imagination. Many aspirants have already established the following links of the bridging antahkarana: 1 . From the physical to the vital or etheric body . This is really an extension of the life thread between the heart and the spleen . 2 . From the physical and the vital, regarding them as a unity, to the astral or emotional vehicle . This thread emanates from, or is anchored in, the solar plexus, and is carried upward by means of the aspiration till it anchors itself in the love petals of the
TL;DR: Lara-Dammer et al. as discussed by the authors proposed a model of how the mind holds geometric imagery in a chunked fashion in what they call the mental plane, which is a hybrid between physical and symbolic, or analog and iconic.
Abstract: The Mental Plane: A Model of Imagining Situations in Euclidean Geometry Francisco Lara-Dammer (flaradam@cs.indiana.edu) Center for Research on Concepts and Cognition, 510 N. Fess Street Bloomington, IN 47408-3822 USA Keywords: Discovery; VSSP; Analog; Iconic. Essentials about the Mental Plane fort. Stronger evidence is given by the cases of famous chess players such as Morphy, Capablanca, and Alekhine, who re- ported headaches after demonstrating blindfold chess, and as a consequence blindfold chess exhibitions were banned in the ex-Soviet Union. (Hooper & Kenneth, 1984). Naturally, more effort is required for the visualization of a compound figure such as an arc with a tangent line than for the visualization of a trivial figure such as a segment. How- ever, the mental plane provides an efficient mechanism: it allows symbolic objects. In this way, for example, the three tangency points of the incircle of a triangle (see Figure 1) are not visualized simultaneously, as happens when we look at a figure drawn on paper. Symbolic mental entities (akin to icons) could be used instead. Therefore, the mental plane is a hybrid between physical and symbolic, or analog and iconic. People process images in their minds all the time. Some- times these images are two-dimensional, as when they play chess or draw a map to describe the location of a place. Some neuroscientists today say that the area in the brain where im- age processing occurs is the Visuospatial Sketchpad (VSSP) (Baddeley, 1995). The goal of this research is to present a model of how the mind holds simple two-dimensional images in the domain of Euclidean geometry, and how this underlies the process of discovery in this microworld. In Euclidean geometry, as in the world of chess, there is an interconnection between external media (e.g., paper) and the mind. It is hypothesized that perception of a figure gives rise to chunks. This poster is about how the mind can hold geometric imagery in a chunked fashion in what we call the mental plane. Two experiences motivated my research in this topic. One was having been defeated in chess by a player moving blind- fold. The other was being a student of a geometry teacher who gave two of his lectures in a pitch-dark room. The teacher was inspired by a famous Swiss geometer of the nine- teenth century who insisted on teaching geometry in pitch- darkness. I give the name mental plane to the place where processing of such abstract imagery occurs in the brain. Its existence becomes obvious when we see students discussing a geometric subject on the phone, or solving a problem while riding their bikes. It is even more striking when we hear of people like Leonhard Euler (1707–1783) who wrote 886 pa- pers of which a significant number were produced in the final two decades of his life, when he was totally blind. The mental plane establishes the basis for what we consider near and far and induces a rough sense of proximity between objects in it. It also gives us a sense of orientation and center, allowing us to discriminate up from down and left from right. None of these notions is numerical. By itself, the mental plane would be useless, but it becomes fully alive when it holds “objects.” The objects of the mental plane are entities such as mental points, mental segments, and mental circles. A crucial principle of the mental plane is economy. I call this the efficiency principle. In order to imagine a geomet- ric figure, the brain needs to supply energy and memory effi- ciently. Therefore, a geometric figure like a circle or segment is not present as a whole most of the time. Instead, the fig- ure is represented partially. If we try to imagine a circle, it is difficult to see the whole thing. With effort it seems possi- ble, but after several seconds the visualization brings discom- Figure 1: The incircle of a triangle. Acknowledgments My research is funded by the Center for Research on Con- cepts and Cognition, Indiana University, Bloomington. References Baddeley, A. (1995). Working memory. In M. S. Gazzaniga (Ed.), The cognitive neurosciences. Cambridge, MA: MIT Press. Eves, H. (1969). An introduction to the history of mathemat- ics. New York: Holt, Rinehart and Winston. Farah, M. (1995). The neural bases of mental imagery. In M. S. Gazzaniga (Ed.), The cognitive neurosciences. Cam- bridge, MA: MIT Press. Hofstadter, D. (1993). A strangely symmetric pattern in- volving conjugacies and “local” and “global” bisectors. (Tech. Rep.). Bloomington, IN: Indiana University, Center for Research on Concepts and Cognition. Hooper, D., & Kenneth, W. (1984). The oxford companion to chess. Oxford: Oxford University Press. Saariluoma, P. (1984). Coding problem spaces in chess. a psychological study. Helsinki, Fin: Societas Scientiarum Fennica.